On Quadrirational Yang-Baxter Maps

We use the classification of the quadrirational maps given by Adler, Bobenko and Suris to describe when such maps satisfy the Yang-Baxter relation. We show that the corresponding maps can be characterized by certain singularity invariance condition. This leads to some new families of Yang-Baxter maps corresponding to the geometric symmetries of pencils of quadrics.Comment: Proceedings of the workshop "Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems" (Glasgow, March-April 2009

Yang-Baxter maps and multi-field integrable lattice equations

A variety of Yang-Baxter maps are obtained from integrable multi-field equations on quad-graphs. A systematic framework for investigating this connection relies on the symmetry groups of the equations. The method is applied to lattice equations introduced by Adler and Yamilov and which are related to the nonlinear superposition formulae for the B\"acklund transformations of the nonlinear Schr\"odinger system and specific ferromagnetic models.Comment: 16 pages, 4 figures, corrected versio

Baryons in the Field Correlator Method: Effects of the Running Strong Coupling

The ground and P-wave excited states of nnn, nns and ssn baryons are studied in the framework of the Field Correlator Method using the running strong coupling constant in the Coulomb-like part of the three-quark potential. The running coupling is calculated up to two loops in the background perturbation theory. The three-quark problem has been solved using the hyperspherical functions method. The masses of the S- and P-wave baryons are presented. Our approach reproduces and improves the previous results for the baryon masses obtained for the freezing value of the coupling constant. The string correction for the confinement potential of the orbitally excited baryons, which is the leading contribution of the proper inertia of the rotating strings, is estimated.Comment: 13 pages, 1 figure, 5 table

Yang Baxter maps with first degree polynomial 2 by 2 Lax matrices

A family of nonparametric Yang Baxter (YB) maps is constructed by refactorization of the product of two 2 by 2 matrix polynomials of first degree. These maps are Poisson with respect to the Sklyanin bracket. For each Casimir function a parametric Poisson YB map is generated by reduction on the corresponding level set. By considering a complete set of Casimir functions symplectic multiparametric YB maps are derived. These maps are quadrirational with explicit formulae in terms of matrix operations. Their Lax matrices are, by construction, 2 by 2 first degree polynomial in the spectral parameter and are classified by Jordan normal form of the leading term. Nonquadrirational parametric YB maps constructed as limits of the quadrirational ones are connected to known integrable systems on quad graphs

Solutions for real dispersionless Veselov-Novikov hierarchy

We investigate the dispersionless Veselov-Novikov (dVN) equation based on the framework of dispersionless two-component BKP hierarchy. Symmetry constraints for real dVN system are considered. It is shown that under symmetry reductions, the conserved densities are therefore related to the associated Faber polynomials and can be solved recursively. Moreover, the method of hodograph transformation as well as the expressions of Faber polynomials are used to find exact real solutions of the dVN hierarchy.Comment: 14 page

Leptonic widths of high excitations in heavy quarkonia

Agreement with the measured electronic widths of the $\psi(4040)$, $\psi(4415)$, and $\Upsilon (11019)$ resonances is shown to be reached if two effects are taken into account: a flattening of the confining potential at large distances and a total screening of the gluon-exchange interaction at r\ga 1.2 fm. The leptonic widths of the unobserved $\Upsilon(7S)$ and $\psi(5S)$ resonances: $\Gamma_{e^+e^-}(\Upsilon (7S))=0.11$ keV and $\Gamma(\psi(5S))\approx 0.54$ keV are predicted.Comment: 11 pages revtex

Spectral Difference Equations Satisfied by KP Soliton Wavefunctions

The Baker-Akhiezer (wave) functions corresponding to soliton solutions of the KP hierarchy are shown to satisfy eigenvalue equations for a commutative ring of translational operators in the spectral parameter. In the rational limit, these translational operators converge to the differential operators in the spectral parameter previously discussed as part of the theory of "bispectrality". Consequently, these translational operators can be seen as demonstrating a form of bispectrality for the non-rational solitons as well.Comment: to appear in "Inverse Problems

Dynamics of quark-gluon plasma from Field correlators

It is argued that strong dynamics in the quark-gluon plasma and bound states of quarks and gluons is mostly due to nonperturbative effects described by field correlators. The emphasis in the paper is made on two explicit calculations of these effects from the first principles: one analytic using gluelump Green's functions and another using independent lattice data on correlators. The resulting hadron spectra are investigated in the range T_c < T < 2T_c. The spectra of charmonia, bottomonia, light s-sbar mesons, glueballs and quark-gluon states calculated numerically are in general agreement with lattice MEM data. The possible role of these bound states in the thermodynamics of quark-gluon plasma is discussed.Comment: Revised version with new comments and references and corrected tables VII-IX; 34 pages + 6 figure

On integrability of Hirota-Kimura type discretizations

We give an overview of the integrability of the Hirota-Kimura discretization method applied to algebraically completely integrable (a.c.i.) systems with quadratic vector fields. Along with the description of the basic mechanism of integrability (Hirota-Kimura bases), we provide the reader with a fairly complete list of the currently available results for concrete a.c.i. systems.Comment: 47 pages, some minor change